Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 8 chapters and video availability01 · Read and understand
What you will learn
- Explain how to extend exponent patterns through zero.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Positive powers and fraction division.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Continue the pattern 5³, 5², 5¹ to find 5⁰ and 5⁻², explaining each division step.
Why this math matters
For a nonzero base, the zero power is one and a negative integer exponent represents a reciprocal. Use negative powers of ten to describe very small quantities without losing their order of magnitude.
Set up the model
A useful answer starts with clear assumptions:
- The base is nonzero.
- Each exponent decreases by one at each step.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Extend exponent patterns through zero
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Continue the pattern 5³, 5², 5¹ to find 5⁰ and 5⁻², explaining each division step.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
5³ = 125; 5² = 25; 5¹ = 5
Reducing the exponent by one divides the value by 5.
Apply the relationship
5⁰ = 5/5 = 1; 5⁻¹ = 1/5
The same division pattern continues through exponent zero.
Check and interpret
5⁻² = (1/5)/5 = 1/25
A negative exponent changes the position of the factor, not the sign of the number.
The result
5⁻² = (1/5)/5 = 1/25
A negative exponent changes the position of the factor, not the sign of the number.
Common mistakes to catch
- A negative exponent does not automatically produce a negative value.
- The nonzero-base condition matters: these rules do not define 0⁻¹.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Evaluate 2⁻³.
Show a hint
Write a reciprocal with a positive exponent.
Reveal answer and explanation
1/8
2⁻³ = 1/(2³) = 1/8.
Practice 2
Simplify (−4)⁰ + (−4)⁻¹.
Show a hint
A nonzero number to power zero is one; keep the negative base in the reciprocal.
Reveal answer and explanation
3/4
1 + 1/(−4) = 1 − 1/4 = 3/4.
Take the idea with you
Use negative powers of ten to describe very small quantities without losing their order of magnitude.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Normalize very small numbers in scientific notation
Completion is your own study record, not a test score. It stays in this browser, does not sync to another device, and can be removed by clearing browser data.